Cost of facilitation: invasive grasses limit recruitment of benefactor shrubs.

ecoblender

alex.filazzola

Abstract

Shrubs facilitate the abundance and productive of annual plants in desert ecosystems.However, these shrub microhabitats favour plant species with competitive life histories. Ephedra californica is a dominant shrub in the San Joaquin desert that has been identified as a facilitator. Here, we explore the factors that limit the Ephedra californica recruitment into the San Joaquin desert including substrate, water availability, and herbivory. We also explore the role of the invasive grass Bromus madritensis on limiting establishment of E. californica. Vegetation surveys were conducted in the field during 2013 and collected seed was then used to conduct two greenhouse trials. The first explore germination and establishment techniques for E. california and the optimal substrate. The second examined E. californica establishment in present of the invasive B. madritensis responding to different water levels and herbivory. These results can have implications for land managers in the San Joaquin Valley to maintain native shrub biodiversity in the region.

---

## load libraries
library(tidyverse)
library(OIsurv)
library(lsmeans)
library(ggthemes)

## load data
substrate <-read.csv("data/Ephedra.substrate.csv")
recruit <-read.csv("data/Ephedra.recruitment.csv")
landscape <-read.csv("data/ephedra.landscape.csv")

##load functions
## inverse hyperbolic sine transformation 
ihs <- function(x) {
    y <- log(x + sqrt(x ^ 2 + 1))
    return(y)
}
se <- function(x, ...) sqrt(var(na.omit(x))/length(na.omit(x)))
source("functions.r")

Ephedra characteristics at the landscape

avg.size <- landscape %>% summarize(H=mean(H), D1=mean(D1), Area=mean(Area), density=mean(Shrub.density), rdm=mean(RDM.2013))
avg.size

##          H       D1     Area     density      rdm
## 1 1.332925 3.446412 9.321902 0.004318859 7.042223

Ephedra recruitment at landscape

## compare ephedra size and density across landscape
landscape[,"area.group"] <- as.numeric(cut(landscape$Log.area,20))
hist(landscape$area.group)

mean.area <- landscape %>% group_by(area.group) %>%  summarize(rdm=mean(RDM.2013), area=mean(Log.area), density=mean(Shrub.density))

ggplot(mean.area) + geom_point(aes(x=density, y=area), size=3)+ylab("log (area of shrub)")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab(expression("shrub density (m"^"2"*")")) +  stat_smooth(method="lm", formula= y~x,aes(x=density, y=area))

m1 <- lm(area~density, data=mean.area)
summary(m1)

## 
## Call:
## lm(formula = area ~ density, data = mean.area)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.82510 -0.26068  0.01197  0.22216  1.16732 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     9.3959     0.9852   9.537 1.84e-08 ***
## density     -1706.0323   223.6888  -7.627 4.81e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5569 on 18 degrees of freedom
## Multiple R-squared:  0.7637, Adjusted R-squared:  0.7506 
## F-statistic: 58.17 on 1 and 18 DF,  p-value: 4.806e-07

ggplot(mean.area) + geom_point(aes(x=density, y=rdm), size=mean.area$area+1)+ylab("residual dry matter")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab(expression("shrub density (m"^"2"*")")) +  stat_smooth(method="lm", formula= y~exp(x),aes(x=density, y=rdm))

m2 <- lm(log(rdm)~density, data=mean.area)
summary(m2)

## 
## Call:
## lm(formula = log(rdm) ~ density, data = mean.area)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32696 -0.09127 -0.02044  0.05849  0.46804 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.1851     0.3294   9.670 1.49e-08 ***
## density     -279.3744    74.7892  -3.735  0.00151 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1862 on 18 degrees of freedom
## Multiple R-squared:  0.4367, Adjusted R-squared:  0.4054 
## F-statistic: 13.95 on 1 and 18 DF,  p-value: 0.001514

Ephedra optimal substrate

substrate[,"Sand"] <- as.factor(substrate$Sand)
substrate[,"census"] <- as.factor(substrate$census)

m1 <- aov(height ~ Micro * Sand,  data=subset(substrate, census==10))
summary(m2) ## nothing significant

## 
## Call:
## lm(formula = log(rdm) ~ density, data = mean.area)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32696 -0.09127 -0.02044  0.05849  0.46804 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.1851     0.3294   9.670 1.49e-08 ***
## density     -279.3744    74.7892  -3.735  0.00151 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1862 on 18 degrees of freedom
## Multiple R-squared:  0.4367, Adjusted R-squared:  0.4054 
## F-statistic: 13.95 on 1 and 18 DF,  p-value: 0.001514

## compare shade on survival of ephedra
my.surv <- Surv(as.numeric(substrate$census), substrate$survival)
fit1 <- survfit(my.surv~Micro, data=substrate)
summary(fit1)

## Call: survfit(formula = my.surv ~ Micro, data = substrate)
## 
##                 Micro=Open 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    960      11    0.989 0.00343        0.982        0.995
##     2    880      29    0.956 0.00681        0.943        0.969
##     3    800      41    0.907 0.00987        0.888        0.927
##     4    720      42    0.854 0.01221        0.830        0.878
##     5    640      67    0.765 0.01504        0.736        0.795
##     6    481      31    0.715 0.01647        0.684        0.748
##     7    400      62    0.604 0.01901        0.568        0.643
##     8    241      31    0.527 0.02108        0.487        0.570
##     9    160      31    0.425 0.02366        0.381        0.474
##    10     80      31    0.260 0.02730        0.212        0.320
## 
##                 Micro=Shade 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    960      33    0.966 0.00588        0.954        0.977
##     2    880      43    0.918 0.00897        0.901        0.936
##     3    800      42    0.870 0.01117        0.849        0.892
##     4    720      40    0.822 0.01290        0.797        0.848
##     5    640      34    0.778 0.01422        0.751        0.807
##     6    480      17    0.751 0.01521        0.721        0.781
##     7    400      31    0.692 0.01725        0.659        0.727
##     8    240      16    0.646 0.01958        0.609        0.686
##     9    160      15    0.586 0.02317        0.542        0.633
##    10     80      13    0.491 0.03099        0.433        0.555

par(mar=c(4.5,4.5,.5,.5))
plot(fit1, col="white", ylim=c(0.2,1), xlim=c(0.9,10.1), ylab="Estimated Survival Function", xlab="Census", cex.lab=1.5, cex.axis=1.3)
lines(1:10,summary(fit1)[[10]][1:10], col="#E69F00", lty=2) ## upper
lines(1:10,summary(fit1)[[6]][1:10], col="#E69F00", lwd=2) ## value sun
lines(1:10,summary(fit1)[[11]][1:10], col="#E69F00", lty=2) ## lower
lines(1:10,summary(fit1)[[10]][11:20], col="#56B4E9", lty=2) ## upper
lines(1:10,summary(fit1)[[6]][11:20], col="#56B4E9", lwd=2) ## value shade
lines(1:10,summary(fit1)[[11]][11:20], col="#56B4E9", lty=2) ## lower
legend(1.8, 0.35, c("Sun","Shade"), lty=1, lwd=3, col=c("#E69F00","#56B4E9"), cex=1.5)

coxph.fit <- coxph(my.surv ~ Micro, method="breslow", data=substrate)
coxph.fit 

## Call:
## coxph(formula = my.surv ~ Micro, data = substrate, method = "breslow")
## 
##               coef exp(coef) se(coef)     z       p
## MicroShade -0.2802    0.7557   0.0786 -3.56 0.00037
## 
## Likelihood ratio test=12.8  on 1 df, p=0.000342
## n= 1920, number of events= 660

## compare sand on survival of ephedra
my.surv <- Surv(as.numeric(substrate$census), substrate$survival)
fit2 <- survfit(my.surv~Sand, data=substrate)
summary(fit2)

## Call: survfit(formula = my.surv ~ Sand, data = substrate)
## 
##                 Sand=0 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    384       7    0.982 0.00683        0.968        0.995
##     2    352      11    0.951 0.01125        0.929        0.973
##     3    320      13    0.912 0.01506        0.883        0.942
##     4    288      12    0.874 0.01799        0.840        0.910
##     5    256      14    0.827 0.02106        0.786        0.869
##     6    192       6    0.801 0.02289        0.757        0.847
##     7    160      12    0.741 0.02695        0.690        0.795
##     8     96       6    0.694 0.03120        0.636        0.758
##     9     64       6    0.629 0.03794        0.559        0.708
##    10     32       6    0.511 0.05325        0.417        0.627
## 
##                 Sand=25 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    384      10    0.974 0.00813        0.958        0.990
##     2    352      16    0.930 0.01331        0.904        0.956
##     3    320      20    0.872 0.01772        0.838        0.907
##     4    288      18    0.817 0.02075        0.777        0.859
##     5    256      15    0.769 0.02292        0.726        0.815
##     6    192       7    0.741 0.02441        0.695        0.791
##     7    160      14    0.676 0.02776        0.624        0.733
##     8     96       7    0.627 0.03137        0.568        0.692
##     9     64       7    0.558 0.03714        0.490        0.636
##    10     32       7    0.436 0.05007        0.348        0.546
## 
##                 Sand=50 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    384      11    0.971 0.00851        0.955        0.988
##     2    352      16    0.927 0.01350        0.901        0.954
##     3    320      19    0.872 0.01765        0.838        0.907
##     4    288      20    0.812 0.02098        0.771        0.854
##     5    256      18    0.755 0.02343        0.710        0.802
##     6    192       9    0.719 0.02512        0.672        0.770
##     7    160      17    0.643 0.02848        0.589        0.701
##     8     96       8    0.589 0.03178        0.530        0.655
##     9     64       8    0.516 0.03697        0.448        0.593
##    10     32       8    0.387 0.04823        0.303        0.494
## 
##                 Sand=75 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    384       9    0.977 0.00772        0.962        0.992
##     2    352      18    0.927 0.01361        0.900        0.954
##     3    320      16    0.880 0.01716        0.847        0.915
##     4    288      17    0.828 0.02025        0.790        0.869
##     5    256      28    0.738 0.02422        0.692        0.787
##     6    192      13    0.688 0.02624        0.638        0.741
##     7    160      26    0.576 0.02976        0.521        0.637
##     8     96      13    0.498 0.03266        0.438        0.566
##     9     64      13    0.397 0.03612        0.332        0.474
##    10     32      13    0.236 0.04058        0.168        0.330
## 
##                 Sand=100 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##     1    384       7    0.982 0.00683        0.968        0.995
##     2    352      11    0.951 0.01125        0.929        0.973
##     3    320      15    0.907 0.01554        0.877        0.937
##     4    288      15    0.859 0.01891        0.823        0.897
##     5    256      26    0.772 0.02349        0.727        0.819
##     6    193      13    0.720 0.02596        0.671        0.773
##     7    160      24    0.612 0.03000        0.556        0.674
##     8     97      13    0.530 0.03351        0.468        0.600
##     9     64      12    0.431 0.03755        0.363        0.511
##    10     32      10    0.296 0.04372        0.222        0.395

test <- substrate %>% group_by(census,Sand) %>%  summarize(count=sum(survival),avg=mean(survival))
test <- data.frame(test)

par(mar=c(4.5,4.5,.5,.5))
plot(fit2, col="white", ylim=c(0.2,1), xlim=c(0.9,10.1), ylab="Estimated Survival Function", xlab="Census", cex.lab=1.5, cex.axis=1.3)
lines(1:10,summary(fit2)[[10]][1:10], col="#E69F00", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][1:10], col="#E69F00", lwd=2) ## value sand 0
lines(1:10,summary(fit2)[[11]][1:10], col="#E69F00", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][11:20], col="#56B4E9", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][11:20], col="#56B4E9", lwd=2) ## value sand 25
lines(1:10,summary(fit2)[[11]][11:20], col="#56B4E9", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][21:30], col="#009E73", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][21:30], col="#009E73", lwd=2) ## value sand 50
lines(1:10,summary(fit2)[[11]][21:30], col="#009E73", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][31:40], col="#CC79A7", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][31:40], col="#CC79A7", lwd=2) ## value sand 75
lines(1:10,summary(fit2)[[11]][31:40], col="#CC79A7", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][41:50], col="#D55E00", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][41:50], col="#D55E00", lwd=2) ## value sand 100
lines(1:10,summary(fit2)[[11]][41:50], col="#D55E00", lty=2) ## lower
legend(1.7, 0.44, c("0%","25%","50%","75%","100%"), lty=1, lwd=3, col=c("#E69F00","#56B4E9","#009E73","#CC79A7","#D55E00"), cex=1.2, title="Sand")

coxph.fit <- coxph(my.surv ~ Sand, method="breslow", data=substrate)
coxph.fit 

## Call:
## coxph(formula = my.surv ~ Sand, data = substrate, method = "breslow")
## 
##          coef exp(coef) se(coef)    z       p
## Sand25  0.263     1.301    0.138 1.91  0.0563
## Sand50  0.365     1.441    0.135 2.71  0.0068
## Sand75  0.579     1.785    0.130 4.47 7.7e-06
## Sand100 0.450     1.568    0.133 3.39  0.0007
## 
## Likelihood ratio test=23.3  on 4 df, p=0.000109
## n= 1920, number of events= 660

## raw number of germinants end trials

end <- subset(substrate, census==10)

## compare microsite

end.means <- end %>% group_by(Micro) %>% summarize(eph=mean(survival), eph.se=se(survival), Height=mean(height, na.rm=T), Height.se=se(height)) %>% gather(measure, value, 2:5) %>% separate(measure, c("Eph",".se")) ## calculate metrics and put long format

## Warning: Too few values at 4 locations: 1, 2, 5, 6

end.means[is.na(end.means$.se),3] <- "mean"
end.means <- end.means %>% spread(.se, value)
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"mean"]-end.means[,"se"]
end.means[,"upper"] <- end.means[,"mean"]+end.means[,"se"]

survival <- subset(end.means, Eph=="eph")

plot1 <- ggplot(survival, aes(x=Micro, y=mean)) + geom_bar(stat="identity") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Microsite") 

height <- subset(end.means, Eph=="Height")

plot2 <- ggplot(height, aes(x=Micro, y=mean)) + geom_bar(stat="identity") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average height of Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Microsite") 

require(gridExtra)

## Loading required package: gridExtra

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

grid.arrange(plot1, plot2, ncol=2)

m1 <- glm(survival~ Sand* Micro, data=end, family="binomial")
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: survival
## 
## Terms added sequentially (first to last)
## 
## 
##            Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                         159     188.21            
## Sand        4   4.7398       155     183.47 0.315056   
## Micro       1  10.7288       154     172.75 0.001055 **
## Sand:Micro  4   8.6588       150     164.09 0.070217 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lsmeans(m1, pairwise~Sand)

## NOTE: Results may be misleading due to involvement in interactions

## $lsmeans
##  Sand     lsmean          SE df   asymp.LCL    asymp.UCL
##  0    -1.4663371   0.4529108 NA   -2.354026  -0.57864819
##  25   -1.3671838   0.4643107 NA   -2.277216  -0.45715153
##  50   -8.7830342 494.5226042 NA -978.029528 960.46345952
##  75   -0.4236489   0.3831780 NA   -1.174664   0.32736619
##  100  -0.8047190   0.3872983 NA   -1.563810  -0.04562817
## 
## Results are averaged over the levels of: Micro 
## Results are given on the logit (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast    estimate          SE df z.ratio p.value
##  0 - 25   -0.09915331   0.6486236 NA  -0.153  0.9999
##  0 - 50    7.31669717 494.5228116 NA   0.015  1.0000
##  0 - 75   -1.04268814   0.5932568 NA  -1.758  0.3987
##  0 - 100  -0.66161811   0.5959263 NA  -1.110  0.8012
##  25 - 50   7.41585049 494.5228222 NA   0.015  1.0000
##  25 - 75  -0.94353482   0.6020048 NA  -1.567  0.5185
##  25 - 100 -0.56246480   0.6046358 NA  -0.930  0.8852
##  50 - 75  -8.35938531 494.5227526 NA  -0.017  1.0000
##  50 - 100 -7.97831529 494.5227559 NA  -0.016  1.0000
##  75 - 100  0.38107003   0.5448168 NA   0.699  0.9567
## 
## Results are averaged over the levels of: Micro 
## Results are given on the log odds ratio (not the response) scale. 
## P value adjustment: tukey method for comparing a family of 5 estimates

## survival
end.means <- end %>% group_by(Sand) %>% summarize(eph=mean(survival), eph.se=se(survival))
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"eph"]-end.means[,"eph.se"]
end.means[,"upper"] <- end.means[,"eph"]+end.means[,"eph.se"]

ggplot(end.means, aes(x=Sand, y=eph)) + geom_bar(stat="identity", fill="#56B4E9") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") 

## height

end.means <- end %>% group_by(Sand) %>% summarize(eph=mean(height, na.rm=T), eph.se=se(height, na.rm=T))
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"eph"]-end.means[,"eph.se"]
end.means[,"upper"] <- end.means[,"eph"]+end.means[,"eph.se"]

ggplot(end.means, aes(x=Sand, y=eph)) + geom_bar(stat="identity", fill="#56B4E9") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") 

## most germinants
maximum.germ <- substrate %>% group_by(Micro, Sand, Rep) %>% summarize(eph.max=max(survival))

max.eph <- maximum.germ %>% group_by(Sand) %>% summarize(eph=mean(eph.max,na.rm=T),eph.se=se(eph.max, na.rm=T)) 
max.eph <- data.frame(max.eph)

max.eph[,"lower"] <- max.eph[,"eph"]-max.eph[,"eph.se"]
max.eph[,"upper"] <- max.eph[,"eph"]+max.eph[,"eph.se"]


ggplot(max.eph, aes(x=Sand, y=eph)) + geom_point(fill="black", size=4) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("total Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") + ylim(0,1) + stat_smooth(method="lm", formula= y~poly(x,2),data=max.eph, aes(x=as.numeric(Sand), y=eph), lwd=1, color="black", lty=2)

m1 <- lm(eph~poly(as.numeric(Sand),2), data=max.eph)
summary(m1)

## 
## Call:
## lm(formula = eph ~ poly(as.numeric(Sand), 2), data = max.eph)
## 
## Residuals:
##        1        2        3        4        5 
## -0.01250  0.01875  0.01875 -0.04375  0.01875 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 0.60625    0.01768  34.295 0.000849 ***
## poly(as.numeric(Sand), 2)1  0.09882    0.03953   2.500 0.129612    
## poly(as.numeric(Sand), 2)2 -0.23385    0.03953  -5.916 0.027402 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03953 on 2 degrees of freedom
## Multiple R-squared:  0.9538, Adjusted R-squared:  0.9075 
## F-statistic: 20.62 on 2 and 2 DF,  p-value: 0.04624

Test of limiting factors - brome

recruit[is.na(recruit)] <- 0

## water
water <- subset(recruit, Treatment == "control" | Treatment=="water")

## germination
water.germ <- water %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(water.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=water, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          299    1275.05             
## Density      1   849.52       298     425.53   <2e-16 ***
## Lvl          2     4.50       296     421.03   0.1053    
## Density:Lvl  2     0.00       294     421.03   0.9985    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## biomass
water.bio <- water %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(water.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## clipping
clip <- subset(recruit, Treatment == "control" | Treatment=="clipped")

## germination
clip.germ <- clip %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(clip.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass
clip.bio <- clip %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(clip.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=clip, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          299    1332.93             
## Density      1   863.30       298     469.63   <2e-16 ***
## Lvl          2     3.66       296     465.97   0.1605    
## Density:Lvl  2     0.04       294     465.93   0.9814    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## shade
shade <- subset(recruit, Treatment == "control" | Treatment=="shade")

## germination
shade.germ <- shade %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(shade.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass
shade.bio <- shade %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(shade.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=shade, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                          299    1221.52              
## Density      1   804.97       298     416.55 < 2.2e-16 ***
## Lvl          2    13.34       296     403.21  0.001267 ** 
## Density:Lvl  2     0.22       294     402.98  0.894507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Test of limiting factors - Ephedra

## water
## germination

ggplot(water.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass

ggplot(water.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## clipping

## germination

ggplot(clip.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass

ggplot(clip.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(ephedra.end~Density *Lvl, data=clip, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     220.71           
## Density      1  2.73641       298     217.97  0.09808 .
## Lvl          2  0.34733       296     217.63  0.84058  
## Density:Lvl  2  0.47792       294     217.15  0.78745  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## shade

## germination

ggplot(shade.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

##biomass
ggplot(shade.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=shade, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                          299    1221.52              
## Density      1   804.97       298     416.55 < 2.2e-16 ***
## Lvl          2    13.34       296     403.21  0.001267 ** 
## Density:Lvl  2     0.22       294     402.98  0.894507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Summarized GLMs for manuscript

## Water
m1 <- glm(ephedra.end~ Density *Lvl, data=water, family=binomial)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     397.45           
## Density      1  2.78375       298     394.66  0.09522 .
## Lvl          2  0.20096       296     394.46  0.90440  
## Density:Lvl  2  0.08676       294     394.37  0.95755  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m1.bio <- glm(Ephedra.biomass~Density *Lvl, data=subset(water, Ephedra.biomass>0 & Ephedra.biomass<0.6), family=Gamma)
anova(m1.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                          106     39.539         
## Density      1  0.11078       105     39.428   0.5364
## Lvl          2  0.10032       103     39.328   0.8411
## Density:Lvl  2  0.53107       101     38.796   0.4001

## Shade
m2 <- glm(ephedra.end~ Density *Lvl, data=shade, family=binomial)
anova(m2, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                          299     368.20            
## Density      1   0.7330       298     367.46 0.391927   
## Lvl          2  11.4709       296     355.99 0.003229 **
## Density:Lvl  2   1.4327       294     354.56 0.488533   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m2.bio <- glm(Ephedra.biomass~Density *Lvl, data=subset(shade, Ephedra.biomass>0 & Ephedra.biomass < 0.7), family=Gamma)
anova(m2.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                           67     25.637           
## Density      1  0.39889        66     25.238  0.23231  
## Lvl          2  2.02160        64     23.217  0.02691 *
## Density:Lvl  2  0.02846        62     23.188  0.95038  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Clipping
m3 <- glm(ephedra.end~ Density *Lvl, data=clip, family=binomial)
anova(m3, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     393.19           
## Density      1   4.2054       298     388.98   0.0403 *
## Lvl          2   0.5545       296     388.43   0.7579  
## Density:Lvl  2   0.8190       294     387.61   0.6640  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m3.bio <- glm(Ephedra.biomass~Density *Lvl, data=subset(clip, Ephedra.biomass>0 & Ephedra.biomass < 0.7), family=Gamma)
anova(m3.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          106     48.613             
## Density      1   0.6174       105     47.996   0.1774    
## Lvl          2   9.2947       103     38.701 1.13e-06 ***
## Density:Lvl  2   0.9905       101     37.711   0.2324    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m4 <-  glm(ephedra.end~brome.begin, data=recruit, family=binomial)
anova(m4, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                          699     901.37         
## brome.begin  1   2.0214       698     899.35   0.1551

m4.bio <-  glm(Ephedra.biomass~brome.begin, data=subset(recruit, Ephedra.biomass>0 & Ephedra.biomass < 0.7), family=Gamma)
anova(m4.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df  Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                           209     89.330         
## brome.begin  1 0.0012905       208     89.328    0.953

## brome comparisons
library(lme4)

## Loading required package: Matrix

## 
## Attaching package: 'Matrix'

## The following object is masked from 'package:tidyr':
## 
##     expand

## Water
m1 <- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(water, Density>0), family=binomial)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                   239     475.39            
## Lvl   2   10.831       237     464.56 0.004447 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Shade
m2 <- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(shade, Density>0), family=binomial)
anova(m2, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                   239     429.07              
## Lvl   2   31.496       237     397.57 1.448e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Clipping
m3<- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(clip, Density>0), family=binomial)
anova(m3, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                   239     528.32           
## Lvl   2    8.962       237     519.35  0.01132 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Brome density vs Ephedra

dense <- recruit %>% filter(Ephedra.biomass>0) %>%  group_by(brome.begin) %>% summarize(bio=mean(Ephedra.biomass), recruit=mean(ephedra.end), germ=mean(ephedra.begin), abv.grd=mean(Ephedra.above),blw.grd=mean(Ephedra.below))

ggplot(dense, aes(x=brome.begin, y=bio))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") + geom_smooth(method=lm, formula= y ~ poly(x,2))

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x
## $y, : font family not found in Windows font database

m1 <- lm(bio~poly(brome.begin,2), data=dense)

## recruitment no effect
ggplot(dense, aes(x=brome.begin, y=recruit))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") #+ geom_smooth(method=lm, formula= y ~ x)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x
## $y, : font family not found in Windows font database

m2 <- lm(recruit~brome.begin, data=dense)

## germination no effect
ggplot(dense, aes(x=brome.begin, y=germ))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") #+ geom_smooth(method=lm, formula= y ~ x)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x
## $y, : font family not found in Windows font database

m3 <- lm(germ~brome.begin, data=dense)


## above ground biomass 
ggplot(dense, aes(x=brome.begin, y=abv.grd))+geom_point()+ theme_Publication() +ylab("above-ground biomass") + xlab("B. madritensis") + geom_smooth(method=lm, formula= y ~ x)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x
## $y, : font family not found in Windows font database

m4 <- lm(abv.grd~brome.begin, data=dense)
summary(m4)

## 
## Call:
## lm(formula = abv.grd ~ brome.begin, data = dense)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.010818 -0.003872 -0.001258  0.004408  0.013263 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.0365715  0.0034310  10.659 4.21e-08 ***
## brome.begin -0.0009681  0.0003850  -2.515   0.0247 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.007263 on 14 degrees of freedom
## Multiple R-squared:  0.3112, Adjusted R-squared:  0.262 
## F-statistic: 6.325 on 1 and 14 DF,  p-value: 0.02474

## below ground biomass
ggplot(dense, aes(x=brome.begin, y=blw.grd))+geom_point()+ theme_Publication() +ylab("below-ground biomass") + xlab("B. madritensis density") + geom_smooth(method=lm, formula= y ~ poly(x,2))

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x
## $y, : font family not found in Windows font database

m5 <- lm(blw.grd~poly(brome.begin,2), data=dense)
summary(m5)

## 
## Call:
## lm(formula = blw.grd ~ poly(brome.begin, 2), data = dense)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0014710 -0.0007298 -0.0001058  0.0005620  0.0015789 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.0049697  0.0002432   20.44 2.89e-11 ***
## poly(brome.begin, 2)1 -0.0036473  0.0009726   -3.75  0.00243 ** 
## poly(brome.begin, 2)2 -0.0032968  0.0009726   -3.39  0.00484 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0009726 on 13 degrees of freedom
## Multiple R-squared:  0.6628, Adjusted R-squared:  0.6109 
## F-statistic: 12.78 on 2 and 13 DF,  p-value: 0.0008538

Germination patterns

recruit

##      ID Treatment   Lvl Rep Density ephedra.emergence branching fluoro
## 1     5   clipped  once   1       0                 0         0 0.0000
## 2    10   clipped  once   2       0                 1         2 0.3215
## 3    13   clipped  once   3       0                 1         6 0.7433
## 4    17   clipped  once   4       0                 0         0 0.0000
## 5    23   clipped  once   5       0                 0         0 0.0000
## 6    26   clipped  once   6       0                 0         0 0.0000
## 7    35   clipped  once   7       0                 0         0 0.0000
## 8    39   clipped  once   8       0                 1         4 0.6366
## 9    44   clipped  once   9       0                 0         0 0.0000
## 10   48   clipped  once  10       0                 0         0 0.0000
## 11   53   clipped  once  11       0                 2         8 0.7806
## 12   56   clipped  once  12       0                 0         0 0.0000
## 13   64   clipped  once  13       0                 0         0 0.0000
## 14   69   clipped  once  14       0                 0         0 0.0000
## 15   74   clipped  once  15       0                 0         0 0.0000
## 16   76   clipped  once  16       0                 0         0 0.0000
## 17   81   clipped  once  17       0                 0         0 0.0000
## 18   86   clipped  once  18       0                 0         0 0.0000
## 19   92   clipped  once  19       0                 0         0 0.0000
## 20   96   clipped  once  20       0                 0         0 0.0000
## 21  105   clipped twice   1       0                 0         0 0.0000
## 22  110   clipped twice   2       0                 1         8 0.7619
## 23  113   clipped twice   3       0                 1         5 0.8012
## 24  117   clipped twice   4       0                 1         4 0.7447
## 25  123   clipped twice   5       0                 2         5 0.7471
## 26  126   clipped twice   6       0                 0         0 0.0000
## 27  135   clipped twice   7       0                 1         4 0.5985
## 28  139   clipped twice   8       0                 1         5 0.7935
## 29  144   clipped twice   9       0                 0         0 0.0000
## 30  148   clipped twice  10       0                 1         6 0.6318
## 31  153   clipped twice  11       0                 1         6 0.6807
## 32  156   clipped twice  12       0                 0         0 0.0000
## 33  164   clipped twice  13       0                 0         0 0.0000
## 34  169   clipped twice  14       0                 0         0 0.0000
## 35  174   clipped twice  15       0                 0         0 0.0000
## 36  176   clipped twice  16       0                 1         4 0.7650
## 37  181   clipped twice  17       0                 0         0 0.0000
## 38  186   clipped twice  18       0                 0         0 0.0000
## 39  192   clipped twice  19       0                 0         0 0.0000
## 40  196   clipped twice  20       0                 0         0 0.0000
## 41    4   clipped  once   1       2                 0         0 0.0000
## 42    9   clipped  once   2       2                 0         0 0.0000
## 43   15   clipped  once   3       2                 0         0 0.0000
## 44   20   clipped  once   4       2                 0         0 0.0000
## 45   21   clipped  once   5       2                 0         0 0.0000
## 46   28   clipped  once   6       2                 0         0 0.0000
## 47   34   clipped  once   7       2                 0         0 0.0000
## 48   38   clipped  once   8       2                 0         0 0.0000
## 49   42   clipped  once   9       2                 0         0 0.0000
## 50   47   clipped  once  10       2                 0         0 0.0000
## 51   52   clipped  once  11       2                 0         0 0.0000
## 52   60   clipped  once  12       2                 0         0 0.0000
## 53   63   clipped  once  13       2                 0         0 0.0000
## 54   70   clipped  once  14       2                 0         0 0.0000
## 55   71   clipped  once  15       2                 1         6 0.7615
## 56   80   clipped  once  16       2                 2         7 0.7943
## 57   83   clipped  once  17       2                 0         0 0.0000
## 58   88   clipped  once  18       2                 0         0 0.0000
## 59   91   clipped  once  19       2                 0         0 0.0000
## 60   98   clipped  once  20       2                 0         0 0.0000
## 61  104   clipped twice   1       2                 1         6 0.6954
## 62  109   clipped twice   2       2                 0         0 0.0000
## 63  115   clipped twice   3       2                 1         4 0.7570
## 64  120   clipped twice   4       2                 0         0 0.0000
## 65  121   clipped twice   5       2                 0         0 0.0000
## 66  128   clipped twice   6       2                 0         0 0.0000
## 67  134   clipped twice   7       2                 0         0 0.0000
## 68  138   clipped twice   8       2                 0         0 0.0000
## 69  142   clipped twice   9       2                 0         0 0.0000
## 70  147   clipped twice  10       2                 0         0 0.0000
## 71  152   clipped twice  11       2                 1         4 0.7681
## 72  160   clipped twice  12       2                 0         0 0.0000
## 73  163   clipped twice  13       2                 0         0 0.0000
## 74  170   clipped twice  14       2                 1         6 0.7063
## 75  171   clipped twice  15       2                 0         0 0.0000
## 76  180   clipped twice  16       2                 1         4 0.7995
## 77  183   clipped twice  17       2                 0         0 0.0000
## 78  188   clipped twice  18       2                 0         0 0.0000
## 79  191   clipped twice  19       2                 0         0 0.0000
## 80  198   clipped twice  20       2                 0         0 0.0000
## 81    3   clipped  once   1       5                 1         3 0.6416
## 82    8   clipped  once   2       5                 0         0 0.0000
## 83   14   clipped  once   3       5                 1         4 0.7920
## 84   18   clipped  once   4       5                 0         0 0.0000
## 85   22   clipped  once   5       5                 0         0 0.0000
## 86   29   clipped  once   6       5                 1         5 0.6169
## 87   32   clipped  once   7       5                 0         0 0.0000
## 88   40   clipped  once   8       5                 1         4 0.6732
## 89   41   clipped  once   9       5                 2         8 0.7775
## 90   49   clipped  once  10       5                 1         5 0.8054
## 91   54   clipped  once  11       5                 2         4 0.7938
## 92   59   clipped  once  12       5                 1         3 0.7967
## 93   62   clipped  once  13       5                 1         5 0.7612
## 94   66   clipped  once  14       5                 1         6 0.7740
## 95   73   clipped  once  15       5                 1        11 0.7853
## 96   77   clipped  once  16       5                 0         0 0.0000
## 97   85   clipped  once  17       5                 0         0 0.0000
## 98   87   clipped  once  18       5                 1         6 0.7532
## 99   95   clipped  once  19       5                 0         0 0.0000
## 100  97   clipped  once  20       5                 1         5 0.7839
## 101 103   clipped twice   1       5                 2         6 0.7245
## 102 108   clipped twice   2       5                 2         6 0.7800
## 103 114   clipped twice   3       5                 0         0 0.0000
## 104 118   clipped twice   4       5                 0         0 0.0000
## 105 122   clipped twice   5       5                 1         4 0.7698
## 106 129   clipped twice   6       5                 0         0 0.0000
## 107 132   clipped twice   7       5                 1         6 0.7884
## 108 140   clipped twice   8       5                 0         0 0.0000
## 109 141   clipped twice   9       5                 0         0 0.0000
## 110 149   clipped twice  10       5                 0         0 0.0000
## 111 154   clipped twice  11       5                 0         0 0.0000
## 112 159   clipped twice  12       5                 0         0 0.0000
## 113 162   clipped twice  13       5                 1         4 0.4452
## 114 166   clipped twice  14       5                 1         7 0.6691
## 115 173   clipped twice  15       5                 0         0 0.0000
## 116 177   clipped twice  16       5                 0         0 0.0000
## 117 185   clipped twice  17       5                 1         4 0.7774
## 118 187   clipped twice  18       5                 0         0 0.0000
## 119 195   clipped twice  19       5                 1         5 0.7694
## 120 197   clipped twice  20       5                 1         4 0.7631
## 121   1   clipped  once   1      10                 1         6 0.7867
## 122   6   clipped  once   2      10                 1         3 0.7592
## 123  12   clipped  once   3      10                 0         0 0.0000
## 124  16   clipped  once   4      10                 0         0 0.0000
## 125  25   clipped  once   5      10                 0         0 0.0000
## 126  27   clipped  once   6      10                 0         0 0.0000
## 127  33   clipped  once   7      10                 1         5 0.7789
## 128  36   clipped  once   8      10                 1         7 0.7092
## 129  43   clipped  once   9      10                 0         0 0.0000
## 130  50   clipped  once  10      10                 0         0 0.0000
## 131  55   clipped  once  11      10                 1         4 0.6851
## 132  58   clipped  once  12      10                 0         0 0.0000
## 133  65   clipped  once  13      10                 0         0 0.0000
## 134  68   clipped  once  14      10                 0         0 0.0000
## 135  75   clipped  once  15      10                 1         4 0.7576
## 136  78   clipped  once  16      10                 1         8 0.7499
## 137  84   clipped  once  17      10                 0         0 0.0000
## 138  90   clipped  once  18      10                 0         0 0.0000
## 139  93   clipped  once  19      10                 0         0 0.0000
## 140  99   clipped  once  20      10                 0         0 0.0000
## 141 101   clipped twice   1      10                 0         0 0.0000
## 142 106   clipped twice   2      10                 1         6 0.7842
## 143 112   clipped twice   3      10                 0         0 0.0000
## 144 116   clipped twice   4      10                 0         0 0.0000
## 145 125   clipped twice   5      10                 0         0 0.0000
## 146 127   clipped twice   6      10                 1         5 0.7753
## 147 133   clipped twice   7      10                 0         0 0.0000
## 148 136   clipped twice   8      10                 0         0 0.0000
## 149 143   clipped twice   9      10                 0         0 0.0000
## 150 150   clipped twice  10      10                 1         5 0.7420
## 151 155   clipped twice  11      10                 0         0 0.0000
## 152 158   clipped twice  12      10                 2         7 0.7999
## 153 165   clipped twice  13      10                 0         0 0.0000
## 154 168   clipped twice  14      10                 3         9 0.6319
## 155 175   clipped twice  15      10                 0         0 0.0000
## 156 178   clipped twice  16      10                 2         5 0.5698
## 157 184   clipped twice  17      10                 0         0 0.0000
## 158 190   clipped twice  18      10                 1         4 0.7780
## 159 193   clipped twice  19      10                 0         0 0.0000
## 160 199   clipped twice  20      10                 0         0 0.0000
## 161   2   clipped  once   1      20                 1         7 0.7863
## 162   7   clipped  once   2      20                 0         0 0.0000
## 163  11   clipped  once   3      20                 0         0 0.0000
## 164  19   clipped  once   4      20                 0         0 0.0000
## 165  24   clipped  once   5      20                 0         0 0.0000
## 166  30   clipped  once   6      20                 0         0 0.0000
## 167  31   clipped  once   7      20                 0         0 0.0000
## 168  37   clipped  once   8      20                 0         0 0.0000
## 169  45   clipped  once   9      20                 0         0 0.0000
## 170  46   clipped  once  10      20                 0         0 0.0000
## 171  51   clipped  once  11      20                 0         0 0.0000
## 172  57   clipped  once  12      20                 0         0 0.0000
## 173  61   clipped  once  13      20                 0         0 0.0000
## 174  67   clipped  once  14      20                 0         0 0.0000
## 175  72   clipped  once  15      20                 0         0 0.0000
## 176  79   clipped  once  16      20                 0         0 0.0000
## 177  82   clipped  once  17      20                 0         0 0.0000
## 178  89   clipped  once  18      20                 0         0 0.0000
## 179  94   clipped  once  19      20                 0         0 0.0000
## 180 100   clipped  once  20      20                 1         4 0.6715
## 181 102   clipped twice   1      20                 0         0 0.0000
## 182 107   clipped twice   2      20                 0         0 0.0000
## 183 111   clipped twice   3      20                 0         0 0.0000
## 184 119   clipped twice   4      20                 0         0 0.0000
## 185 124   clipped twice   5      20                 0         0 0.0000
## 186 130   clipped twice   6      20                 1         5 0.5799
## 187 131   clipped twice   7      20                 0         0 0.0000
## 188 137   clipped twice   8      20                 0         0 0.0000
## 189 145   clipped twice   9      20                 1         3 0.7009
## 190 146   clipped twice  10      20                 0         0 0.0000
## 191 151   clipped twice  11      20                 1         5 0.7652
## 192 157   clipped twice  12      20                 0         0 0.0000
## 193 161   clipped twice  13      20                 0         0 0.0000
## 194 167   clipped twice  14      20                 0         0 0.0000
## 195 172   clipped twice  15      20                 0         0 0.0000
## 196 179   clipped twice  16      20                 0         0 0.0000
## 197 182   clipped twice  17      20                 2         6 0.7488
## 198 189   clipped twice  18      20                 0         0 0.0000
## 199 194   clipped twice  19      20                 0         0 0.0000
## 200 200   clipped twice  20      20                 0         0 0.0000
## 201 205   control  none   1       0                 0         0 0.0000
## 202 210   control  none   2       0                 0         0 0.0000
## 203 213   control  none   3       0                 1         5 0.7908
## 204 217   control  none   4       0                 1         3 0.7910
## 205 223   control  none   5       0                 0         0 0.0000
## 206 226   control  none   6       0                 0         0 0.0000
## 207 235   control  none   7       0                 1         6 0.7779
## 208 239   control  none   8       0                 0         0 0.0000
## 209 244   control  none   9       0                 1         6 0.5830
## 210 248   control  none  10       0                 1         5 0.7768
## 211 253   control  none  11       0                 0         0 0.0000
## 212 256   control  none  12       0                 0         0 0.0000
## 213 264   control  none  13       0                 0         0 0.0000
## 214 269   control  none  14       0                 0         0 0.0000
## 215 274   control  none  15       0                 0         0 0.0000
## 216 276   control  none  16       0                 1         4 0.7781
## 217 281   control  none  17       0                 0         0 0.0000
## 218 286   control  none  18       0                 0         0 0.0000
## 219 292   control  none  19       0                 0         0 0.0000
## 220 296   control  none  20       0                 0         0 0.0000
## 221 204   control  none   1       2                 1         9 0.6990
## 222 209   control  none   2       2                 0         0 0.0000
## 223 215   control  none   3       2                 0         0 0.0000
## 224 220   control  none   4       2                 0         0 0.0000
## 225 221   control  none   5       2                 0         0 0.0000
## 226 228   control  none   6       2                 0         0 0.0000
## 227 234   control  none   7       2                 1         5 0.7909
## 228 238   control  none   8       2                 0         0 0.0000
## 229 242   control  none   9       2                 1         5 0.7632
## 230 247   control  none  10       2                 0         0 0.0000
## 231 252   control  none  11       2                 1         7 0.8060
## 232 260   control  none  12       2                 1         7 0.7774
## 233 263   control  none  13       2                 0         0 0.0000
## 234 270   control  none  14       2                 0         0 0.0000
## 235 271   control  none  15       2                 1         6 0.7727
## 236 280   control  none  16       2                 0         0 0.0000
## 237 283   control  none  17       2                 2         5 0.7937
## 238 288   control  none  18       2                 0         0 0.0000
## 239 291   control  none  19       2                 1         3 0.4486
## 240 298   control  none  20       2                 0         0 0.0000
## 241 203   control  none   1       5                 0         0 0.0000
## 242 208   control  none   2       5                 0         0 0.0000
## 243 214   control  none   3       5                 0         0 0.0000
## 244 218   control  none   4       5                 0         0 0.0000
## 245 222   control  none   5       5                 0         0 0.0000
## 246 229   control  none   6       5                 1         6 0.8044
## 247 232   control  none   7       5                 1         3 0.8003
## 248 240   control  none   8       5                 0         0 0.0000
## 249 241   control  none   9       5                 1         3 0.4088
## 250 249   control  none  10       5                 0         0 0.0000
## 251 254   control  none  11       5                 0         0 0.0000
## 252 259   control  none  12       5                 0         0 0.0000
## 253 262   control  none  13       5                 1         9 0.7871
## 254 266   control  none  14       5                 2         5 0.7579
## 255 273   control  none  15       5                 0         0 0.0000
## 256 277   control  none  16       5                 1         3 0.7850
## 257 285   control  none  17       5                 2         8 0.7973
## 258 287   control  none  18       5                 0         0 0.0000
## 259 295   control  none  19       5                 1         5 0.7066
## 260 297   control  none  20       5                 0         0 0.0000
## 261 201   control  none   1      10                 0         0 0.0000
## 262 206   control  none   2      10                 1         5 0.7773
## 263 212   control  none   3      10                 0         0 0.0000
## 264 216   control  none   4      10                 0         0 0.0000
## 265 225   control  none   5      10                 0         0 0.0000
## 266 227   control  none   6      10                 1         7 0.7974
## 267 233   control  none   7      10                 2         3 0.6053
## 268 236   control  none   8      10                 0         0 0.0000
## 269 243   control  none   9      10                 0         0 0.0000
## 270 250   control  none  10      10                 0         0 0.0000
## 271 255   control  none  11      10                 2         7 0.7887
## 272 258   control  none  12      10                 0         0 0.0000
## 273 265   control  none  13      10                 0         0 0.0000
## 274 268   control  none  14      10                 0         0 0.0000
## 275 275   control  none  15      10                 1         7 0.7880
## 276 278   control  none  16      10                 0         0 0.0000
## 277 284   control  none  17      10                 1         4 0.7938
## 278 290   control  none  18      10                 0         0 0.0000
## 279 293   control  none  19      10                 0         0 0.0000
## 280 299   control  none  20      10                 0         0 0.0000
## 281 202   control  none   1      20                 1         3 0.7360
## 282 207   control  none   2      20                 1         5 0.7544
## 283 211   control  none   3      20                 0         0 0.0000
## 284 219   control  none   4      20                 0         0 0.0000
## 285 224   control  none   5      20                 0         0 0.0000
## 286 230   control  none   6      20                 0         0 0.0000
## 287 231   control  none   7      20                 2         5 0.6865
## 288 237   control  none   8      20                 1         3 0.7434
## 289 245   control  none   9      20                 0         0 0.0000
## 290 246   control  none  10      20                 0         0 0.0000
## 291 251   control  none  11      20                 0         0 0.0000
## 292 257   control  none  12      20                 2         5 0.5452
## 293 261   control  none  13      20                 0         0 0.0000
## 294 267   control  none  14      20                 0         0 0.0000
## 295 272   control  none  15      20                 0         0 0.0000
## 296 279   control  none  16      20                 0         0 0.0000
## 297 282   control  none  17      20                 0         0 0.0000
## 298 289   control  none  18      20                 0         0 0.0000
## 299 294   control  none  19      20                 0         0 0.0000
## 300 300   control  none  20      20                 2         7 0.7728
## 301 305     shade  high   1       0                 0         0 0.0000
## 302 310     shade  high   2       0                 0         0 0.0000
## 303 313     shade  high   3       0                 0         0 0.0000
## 304 317     shade  high   4       0                 1         3 0.6200
## 305 323     shade  high   5       0                 0         0 0.0000
## 306 326     shade  high   6       0                 0         0 0.0000
## 307 335     shade  high   7       0                 0         0 0.0000
## 308 339     shade  high   8       0                 0         0 0.0000
## 309 344     shade  high   9       0                 0         0 0.0000
## 310 348     shade  high  10       0                 0         0 0.0000
## 311 353     shade  high  11       0                 0         0 0.0000
## 312 356     shade  high  12       0                 0         0 0.0000
## 313 364     shade  high  13       0                 0         0 0.0000
## 314 369     shade  high  14       0                 0         0 0.0000
## 315 374     shade  high  15       0                 0         0 0.0000
## 316 376     shade  high  16       0                 0         0 0.0000
## 317 381     shade  high  17       0                 0         0 0.0000
## 318 386     shade  high  18       0                 0         0 0.0000
## 319 392     shade  high  19       0                 0         0 0.0000
## 320 396     shade  high  20       0                 1         3 0.8874
## 321 405     shade   med   1       0                 0         0 0.0000
## 322 410     shade   med   2       0                 0         0 0.0000
## 323 413     shade   med   3       0                 0         0 0.0000
## 324 417     shade   med   4       0                 0         0 0.0000
## 325 423     shade   med   5       0                 0         0 0.0000
## 326 426     shade   med   6       0                 1         8 0.7693
## 327 435     shade   med   7       0                 1         7 0.7306
## 328 439     shade   med   8       0                 0         0 0.0000
## 329 444     shade   med   9       0                 0         0 0.0000
## 330 448     shade   med  10       0                 0         0 0.0000
## 331 453     shade   med  11       0                 0         0 0.0000
## 332 456     shade   med  12       0                 0         0 0.0000
## 333 464     shade   med  13       0                 0         0 0.0000
## 334 469     shade   med  14       0                 0         0 0.0000
## 335 474     shade   med  15       0                 0         0 0.0000
## 336 476     shade   med  16       0                 0         0 0.0000
## 337 481     shade   med  17       0                 0         0 0.0000
## 338 486     shade   med  18       0                 1         7 0.7961
## 339 492     shade   med  19       0                 0         0 0.0000
## 340 496     shade   med  20       0                 0         0 0.0000
## 341 304     shade  high   1       2                 0         0 0.0000
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##     brome.begin brome.prop.begin ephedra.begin ephedra.end brome.respawn
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## 623           6               60             0           0             0
## 624           6               60             1           1             0
## 625           6               60             0           0             0
## 626           5               50             0           0             0
## 627           7               70             1           1             0
## 628           5               50             0           0             0
## 629           8               80             1           1             0
## 630           6               60             0           0             0
## 631           8               80             1           0             0
## 632           5               50             1           1             0
## 633           5               50             0           0             0
## 634           6               60             0           0             0
## 635           9               90             0           0             3
## 636           6               60             0           0             0
## 637           1               10             1           1             0
## 638           4               40             1           0             2
## 639           5               50             1           0             0
## 640           5               50             0           0             0
## 641           7               70             1           1             0
## 642           4               40             1           1             0
## 643           7               70             1           0             0
## 644           7               70             0           0             0
## 645           8               80             1           1             0
## 646          10              100             0           0             0
## 647           8               80             1           1             0
## 648           5               50             1           1             0
## 649           6               60             0           0             0
## 650          10              100             0           0             0
## 651           7               70             0           0             0
## 652           4               40             0           0             0
## 653           7               70             1           1             0
## 654           6               60             1           1             0
## 655           3               30             0           0             0
## 656           7               70             1           1             0
## 657           7               70             0           0             0
## 658           4               40             1           1             1
## 659           7               70             0           0             1
## 660           7               70             0           0             0
## 661          12               60             1           0             0
## 662          13               65             1           1             0
## 663          13               65             1           1             0
## 664           8               40             1           1             0
## 665          15               75             1           1             0
## 666           5               25             1           0             0
## 667          13               65             1           0             1
## 668           7               35             1           1             0
## 669           8               40             0           0             0
## 670           7               35             1           0             0
## 671           6               30             0           0             0
## 672           1                5             1           1             0
## 673           8               40             1           0             0
## 674          13               65             0           0             0
## 675          11               55             1           0             0
## 676          11               55             0           0             0
## 677          10               50             1           1             0
## 678          13               65             0           0             4
## 679          11               55             0           0             0
## 680          12               60             0           0             0
## 681           7               35             0           0             0
## 682          10               50             1           1             0
## 683          15               75             0           0             0
## 684          14               70             1           1             0
## 685          10               50             1           1             1
## 686          15               75             1           0             1
## 687           8               40             0           0             0
## 688          13               65             0           0             0
## 689          13               65             1           0             0
## 690          12               60             1           0             0
## 691          10               50             0           0             0
## 692           7               35             0           0             0
## 693          12               60             1           1             2
## 694           8               40             0           0             0
## 695           9               45             0           0             0
## 696          13               65             0           0             1
## 697          11               55             1           0             0
## 698          13               65             1           1             2
## 699          14               70             0           0             0
## 700          10               50             1           1             0
##     Ephedra.above Ephedra.below Ephedra.biomass brome.biomass
## 1         0.00550       0.00120         0.00670       0.00000
## 2         0.02650       0.00350         0.03000       0.09180
## 3         0.01360       0.00510         0.01870       0.25030
## 4         0.00000       0.00000         0.00000       0.00000
## 5         0.02130       0.00530         0.02660       0.12160
## 6         0.00000       0.00000         0.00000       0.29580
## 7         0.00000       0.00000         0.00000       0.26070
## 8         0.01650       0.00820         0.02470       0.18090
## 9         0.00000       0.00000         0.00000       0.20730
## 10        0.00000       0.00000         0.00000       0.28800
## 11        0.00000       0.00000         0.00000       0.00000
## 12        0.03620       0.00600         0.04220       0.37190
## 13        0.00000       0.00000         0.00000       0.05550
## 14        0.00000       0.00000         0.00000       0.00000
## 15        0.00000       0.00000         0.00000       0.19680
## 16        0.00000       0.00000         0.00000       0.00000
## 17        0.02370       0.00460         0.02830       0.09410
## 18        0.00000       0.00000         0.00000       0.64990
## 19        0.00000       0.00000         0.00000       0.37030
## 20        0.00000       0.00000         0.00000       0.38870
## 21        0.00000       0.00000         0.00000       0.10390
## 22        0.00000       0.00000         0.00000       0.12920
## 23        0.01850       0.00000         0.01850       0.08190
## 24        0.01300       0.00080         0.01380       0.00000
## 25        0.00000       0.00000         0.00000       0.20410
## 26        0.00000       0.00000         0.00000       0.12900
## 27        0.00000       0.00000         0.00000       0.11510
## 28        0.01280       0.00530         0.01810       0.07580
## 29        0.00000       0.00000         0.00000       0.10430
## 30        0.02450       0.00260         0.02710       0.30570
## 31        0.03030       0.00830         0.03860       0.00000
## 32        0.04260       0.00930         0.05190       0.22820
## 33        0.00000       0.00000         0.00000       0.16880
## 34        0.00930       0.00320         0.01250       0.00000
## 35        0.00000       0.00000         0.00000       0.63810
## 36        0.01810       0.00310         0.02120       0.00000
## 37        0.01650       0.00270         0.01920       0.05580
## 38        0.01550       0.00080         0.01630       0.25570
## 39        0.00000       0.00000         0.00000       0.31530
## 40        0.00000       0.00000         0.00000       0.43460
## 41        0.01070       0.00080         0.01150       0.28450
## 42        0.00000       0.00000         0.00000       0.18080
## 43        0.00000       0.00000         0.00000       0.00000
## 44        0.00000       0.00000         0.00000       0.51090
## 45        0.00000       0.00000         0.00000       0.49770
## 46        0.00000       0.00000         0.00000       0.37290
## 47        0.00000       0.00000         0.00000       0.00000
## 48        0.02490       0.00640         0.03130       0.48910
## 49        0.00000       0.00000         0.00000       0.26980
## 50        0.03850       0.00740         0.04590       0.09020
## 51        0.00000       0.00000         0.00000       0.06860
## 52        0.00000       0.00000         0.00000       0.00000
## 53        0.00000       0.00000         0.00000       0.04360
## 54        0.00000       0.00000         0.00000       0.04860
## 55        0.00000       0.00000         0.00000       0.34990
## 56        0.00000       0.00000         0.00000       0.08430
## 57        0.00000       0.00000         0.00000       0.05540
## 58        0.01160       0.00350         0.01510       0.42220
## 59        0.05680       0.00790         0.06470       0.08060
## 60        0.00000       0.00000         0.00000       0.14490
## 61        0.04010       0.01200         0.05210       0.22380
## 62        0.02610       0.01290         0.03900       0.07840
## 63        0.00000       0.00000         0.00000       0.00000
## 64        0.01410       0.00560         0.01970       0.10500
## 65        0.01290       0.00410         0.01700       0.31520
## 66        0.03570       0.00750         0.04320       0.13820
## 67        0.00000       0.00000         0.00000       0.00000
## 68        0.00000       0.00000         0.00000       0.08840
## 69        0.00000       0.00000         0.00000       0.20450
## 70        0.00900       0.00360         0.01260       0.05780
## 71        0.00000       0.00000         0.00000       0.07440
## 72        0.00900       0.00250         0.01150       0.32930
## 73        0.00000       0.00000         0.00000       0.03150
## 74        0.00990       0.00500         0.01490       0.00000
## 75        0.00000       0.00000         0.00000       0.29070
## 76        0.00000       0.00000         0.00000       0.06400
## 77        0.00000       0.00000         0.00000       0.36160
## 78        0.00000       0.00000         0.00000       0.08940
## 79        0.02130       0.00510         0.02640       0.06920
## 80        0.00000       0.00000         0.00000       0.14790
## 81        0.00000       0.00000         0.00000       0.97380
## 82        0.00000       0.00000         0.00000       0.07510
## 83        0.00000       0.00000         0.00000       0.00000
## 84        0.02700       0.00230         0.02930       0.37440
## 85        0.00000       0.00000         0.00000       0.00000
## 86        0.03300       0.00550         0.03850       0.05470
## 87        0.00000       0.00000         0.00000       0.28710
## 88        0.00000       0.00000         0.00000       0.13070
## 89        0.00000       0.00000         0.00000       0.00000
## 90        0.00000       0.00000         0.00000       0.00000
## 91        0.04280       0.00770         0.05050       0.14800
## 92        0.00000       0.00000         0.00000       0.00000
## 93        0.00000       0.00000         0.00000       0.06470
## 94        0.00000       0.00000         0.00000       0.36080
## 95        0.00000       0.00000         0.00000       0.00000
## 96        0.00560       0.00270         0.00830       0.48060
## 97        0.00000       0.00000         0.00000       0.18510
## 98        0.00000       0.00000         0.00000       0.03410
## 99        0.00850       0.00180         0.01030       0.24800
## 100       0.01120       0.00560         0.01680       0.12510
## 101       0.00000       0.00000         0.00000       0.22280
## 102       0.00000       0.00000         0.00000       0.27740
## 103       0.00000       0.00000         0.00000       0.00000
## 104       0.00000       0.00000         0.00000       0.16200
## 105       0.01540       0.00220         0.01760       0.00000
## 106       0.00000       0.00000         0.00000       0.13150
## 107       0.01820       0.00520         0.02340       0.13440
## 108       0.04970       0.01330         0.06300       0.19300
## 109       0.01480       0.00230         0.01710       0.00000
## 110       0.01200       0.00220         0.01420       0.04960
## 111       0.00000       0.00000         0.00000       0.15610
## 112       0.00000       0.00000         0.00000       0.49510
## 113       0.00820       0.00220         0.01040       0.07590
## 114       0.00000       0.00000         0.00000       0.55020
## 115       0.00000       0.00000         0.00000       0.00000
## 116       0.00000       0.00000         0.00000       0.74260
## 117       0.00000       0.00000         0.00000       0.23590
## 118       0.00000       0.00000         0.00000       0.06120
## 119       0.00150       0.00160         0.00310       0.09730
## 120       0.00000       0.00000         0.00000       0.07230
## 121       0.02430       0.00680         0.03110       0.34550
## 122       0.00000       0.00000         0.00000       0.08370
## 123       0.00000       0.00000         0.00000       0.52100
## 124       0.02340       0.00480         0.02820       0.17470
## 125       0.00000       0.00000         0.00000       0.00000
## 126       0.00000       0.00000         0.00000       0.36200
## 127       0.00000       0.00000         0.00000       0.00000
## 128       0.00000       0.00000         0.00000       0.11290
## 129       0.02560       0.00530         0.03090       0.11980
## 130       0.01280       0.00260         0.01540       0.29680
## 131       0.00000       0.00000         0.00000       0.03630
## 132       0.01900       0.00490         0.02390       0.12700
## 133       0.02270       0.00920         0.03190       0.03560
## 134       0.04150       0.00480         0.04630       0.31550
## 135       0.00000       0.00000         0.00000       0.00000
## 136       0.00000       0.00000         0.00000       0.00000
## 137       0.00000       0.00000         0.00000       0.10080
## 138       0.00000       0.00000         0.00000       0.00000
## 139       0.00000       0.00000         0.00000       0.75300
## 140       0.00000       0.00000         0.00000       0.11050
## 141       0.00000       0.00000         0.00000       0.11840
## 142       0.02530       0.00610         0.03140       0.07840
## 143       0.00000       0.00000         0.00000       0.04040
## 144       0.00000       0.00000         0.00000       0.21310
## 145       0.00820       0.00490         0.01310       0.00000
## 146       0.00300       0.00060         0.00360       0.20720
## 147       0.00000       0.00000         0.00000       0.11400
## 148       0.00000       0.00000         0.00000       0.06970
## 149       0.00000       0.00000         0.00000       0.08230
## 150       0.00000       0.00000         0.00000       0.26620
## 151       0.00000       0.00000         0.00000       0.05840
## 152       0.00000       0.00000         0.00000       0.04610
## 153       0.00000       0.00000         0.00000       0.09150
## 154       0.00000       0.00000         0.00000       0.50060
## 155       0.00000       0.00000         0.00000       0.00000
## 156       0.00000       0.00000         0.00000       0.00000
## 157       0.00000       0.00000         0.00000       0.11740
## 158       0.01170       0.00270         0.01440       0.00000
## 159       0.00000       0.00000         0.00000       0.40220
## 160       0.01240       0.00200         0.01440       0.05850
## 161       0.00000       0.00000         0.00000       0.75040
## 162       0.06560       0.01170         0.07730       0.00000
## 163       0.00000       0.00000         0.00000       0.00000
## 164       0.03600       0.00780         0.04380       0.13120
## 165       0.00000       0.00000         0.00000       0.33800
## 166       0.01150       0.00230         0.01380       0.12240
## 167       0.00000       0.00000         0.00000       0.22720
## 168       0.00000       0.00000         0.00000       0.18500
## 169       0.03550       0.00100         0.03650       0.14660
## 170       0.01950       0.00380         0.02330       0.29450
## 171       0.00810       0.00500         0.01310       0.40970
## 172       0.01220       0.00430         0.01650       0.00000
## 173       0.00000       0.00000         0.00000       0.35110
## 174       0.00000       0.00000         0.00000       0.59720
## 175       0.00000       0.00000         0.00000       0.00000
## 176       0.00000       0.00000         0.00000       0.00000
## 177       0.00000       0.00000         0.00000       0.20830
## 178       0.00000       0.00000         0.00000       0.00000
## 179       0.00000       0.00000         0.00000       0.00000
## 180       0.00000       0.00000         0.00000       0.14880
## 181       0.00770       0.00000         0.00770       0.16940
## 182       0.01310       0.00270         0.01580       0.00000
## 183       0.00000       0.00000         0.00000       0.00000
## 184       0.00000       0.00000         0.00000       0.08240
## 185       0.00000       0.00000         0.00000       0.22150
## 186       0.00720       0.00080         0.00800       0.08980
## 187       0.00000       0.00000         0.00000       0.05690
## 188       0.00000       0.00000         0.00000       0.05500
## 189       0.00000       0.00000         0.00000       0.63270
## 190       0.00000       0.00000         0.00000       0.30780
## 191       0.03100       0.00870         0.03970       0.23010
## 192       0.01410       0.00130         0.01540       0.00000
## 193       0.01750       0.00130         0.01880       0.46290
## 194       0.01240       0.00260         0.01500       0.21450
## 195       0.00000       0.00000         0.00000       0.00000
## 196       0.00000       0.00000         0.00000       0.00000
## 197       0.00000       0.00000         0.00000       0.52390
## 198       0.00000       0.00000         0.00000       0.00000
## 199       0.00000       0.00000         0.00000       0.05120
## 200       0.01320       0.00140         0.01460       0.00000
## 201       0.00000       0.00000         0.00000       0.26740
## 202       0.01110       0.00190         0.01300       0.15880
## 203       0.03880       0.00270         0.04150       0.10360
## 204       0.00000       0.00000         0.00000       0.00000
## 205       0.00000       0.00000         0.00000       0.00000
## 206       0.03070       0.00230         0.03300       0.12130
## 207       0.00000       0.00000         0.00000       0.19280
## 208       0.00000       0.00000         0.00000       0.17980
## 209       0.69900       0.01180         0.07180       0.79270
## 210       0.03840       0.00690         0.04530       0.58480
## 211       0.00000       0.00000         0.00000       0.00000
## 212       0.00000       0.00000         0.00000       0.54080
## 213       0.00000       0.00000         0.00000       0.28460
## 214       0.04600       0.00760         0.05360       0.00000
## 215       0.00000       0.00000         0.00000       0.64600
## 216       0.02830       0.00550         0.03380       0.00000
## 217       0.00000       0.00000         0.00000       0.18060
## 218       0.00000       0.00000         0.00000       0.51500
## 219       0.00000       0.00000         0.00000       0.47590
## 220       0.00000       0.00000         0.00000       0.62080
## 221       0.01240       0.00530         0.01770       0.33220
## 222       0.08860       0.01020         0.09880       0.24710
## 223       0.00000       0.00000         0.00000       0.23960
## 224       0.00350       0.00000         0.00350       0.47170
## 225       0.04330       0.00440         0.04770       0.26980
## 226       0.03900       0.00650         0.04550       0.44520
## 227       0.00000       0.00000         0.00000       0.07190
## 228       0.00000       0.00000         0.00000       0.25540
## 229       0.00000       0.00000         0.00000       0.56060
## 230       0.05980       0.00940         0.06920       0.48800
## 231       0.03560       0.00410         0.03970       0.01880
## 232       0.05700       0.01200         0.06900       0.70010
## 233       0.00000       0.00000         0.00000       0.09610
## 234       0.00000       0.00000         0.00000       0.08420
## 235       0.00000       0.00000         0.00000       0.19430
## 236       0.05690       0.01030         0.06720       0.16430
## 237       0.00000       0.00000         0.00000       0.10320
## 238       0.03300       0.00790         0.04090       0.25460
## 239       0.00000       0.00000         0.00000       0.15270
## 240       0.02760       0.00770         0.03530       0.19710
## 241       0.00000       0.00000         0.00000       0.40440
## 242       0.06080       0.01290         0.07370       0.34680
## 243       0.00000       0.00000         0.00000       0.00000
## 244       0.01850       0.00410         0.02260       0.12600
## 245       0.03220       0.00850         0.04070       0.00000
## 246       0.00000       0.00000         0.00000       0.72250
## 247       0.00000       0.00000         0.00000       0.58350
## 248       0.01660       0.00140         0.01800       0.22040
## 249       0.03030       0.00380         0.03410       0.00000
## 250       0.03990       0.00470         0.04460       0.00000
## 251       0.00000       0.00000         0.00000       0.21270
## 252       0.00000       0.00000         0.00000       0.14510
## 253       0.00000       0.00000         0.00000       0.07130
## 254       0.00000       0.00000         0.00000       0.55520
## 255       0.00000       0.00000         0.00000       0.00000
## 256       0.00000       0.00000         0.00000       0.58590
## 257       0.00000       0.00000         0.00000       0.20620
## 258       0.00000       0.00000         0.00000       0.21800
## 259       0.00000       0.00000         0.00000       0.13050
## 260       0.00000       0.00000         0.00000       0.21200
## 261       0.00000       0.00000         0.00000       0.39010
## 262       0.01580       0.00400         0.01980       0.18070
## 263       0.00000       0.00000         0.00000       0.08230
## 264       0.04550       0.00490         0.05040       0.31070
## 265       0.06410       0.01890         0.08300       0.00000
## 266       0.00000       0.00000         0.00000       0.61500
## 267       0.00000       0.00000         0.00000       0.00000
## 268       0.00000       0.00000         0.00000       0.07120
## 269       0.03720       0.00550         0.04270       0.32410
## 270       0.06100       0.01660         0.07760       0.21200
## 271       0.00000       0.00000         0.00000       0.09400
## 272       0.00000       0.00000         0.00000       0.16790
## 273       0.06320       0.00790         0.07110       0.15580
## 274       0.00000       0.00000         0.00000       0.33890
## 275       0.00000       0.00000         0.00000       0.00000
## 276       0.00000       0.00000         0.00000       0.00000
## 277       0.00920       0.00210         0.01130       0.13280
## 278       0.00000       0.00000         0.00000       0.00000
## 279       0.00000       0.00000         0.00000       0.23810
## 280       0.02680       0.00730         0.03410       0.07970
## 281       0.00000       0.00000         0.00000       0.40410
## 282       0.00000       0.00000         0.00000       0.00000
## 283       0.00000       0.00000         0.00000       0.00000
## 284       0.00000       0.00000         0.00000       0.53350
## 285       0.00000       0.00000         0.00000       0.64980
## 286       0.03330       0.00000         0.03330       0.43210
## 287       0.00000       0.00610         0.00610       0.11750
## 288       0.00000       0.00000         0.00000       0.18620
## 289       0.04940       0.01460         0.06400       0.63010
## 290       0.00000       0.00000         0.00000       0.42480
## 291       0.00000       0.00000         0.00000       0.19640
## 292       0.00000       0.00000         0.00000       0.00000
## 293       0.00000       0.00000         0.00000       0.40760
## 294       0.01220       0.00270         0.01490       0.24880
## 295       0.00000       0.00000         0.00000       0.00000
## 296       0.00000       0.00000         0.00000       0.00000
## 297       0.00000       0.00000         0.00000       0.35760
## 298       0.00000       0.00000         0.00000       0.00000
## 299       0.00000       0.00000         0.00000       0.17540
## 300       0.00000       0.00000         0.00000       0.26390
## 301       0.03520       0.00490         0.04010       0.13690
## 302       0.00000       0.00000         0.00000       0.11630
## 303       0.00000       0.00000         0.00000       0.13920
## 304       0.00000       0.00000         0.00000       0.00000
## 305       0.00000       0.00000         0.00000       0.10280
## 306       0.03260       0.00080         0.03340       0.03700
## 307       0.00000       0.00000         0.00000       0.13280
## 308       0.00000       0.00000         0.00000       0.09610
## 309       0.00000       0.00000         0.00000       0.28290
## 310       0.00000       0.00000         0.00000       0.00000
## 311       0.00000       0.00000         0.00000       0.00000
## 312       0.00000       0.00000         0.00000       0.22240
## 313       0.02280       0.00570         0.02850       0.23670
## 314       0.00000       0.00000         0.00000       0.00000
## 315       0.00000       0.00000         0.00000       0.25500
## 316       0.02230       0.00270         0.02500       0.00000
## 317       0.00000       0.00000         0.00000       0.07660
## 318       0.00000       0.00000         0.00000       0.23500
## 319       0.00000       0.00000         0.00000       0.13050
## 320       0.00000       0.00000         0.00000       0.00000
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## 693       0.05940       0.00390         0.06330       0.48940
## 694       0.00000       0.00000         0.00000       1.04530
## 695       0.00000       0.00000         0.00000       0.00000
## 696       0.00000       0.00000         0.00000       0.08600
## 697       0.05310       0.00380         0.05690       2.10530
## 698       0.05120       0.00950         0.06070       0.00000
## 699       0.00000       0.00000         0.00000       0.65810
## 700       0.02370       0.00400         0.02770       0.27220

recruit[is.na(recruit)] <- 0

recruit[,"eph.rate"] <- recruit$ephedra.emergence/3*100

## Percent of ephedra seedlings becoming established
mean(recruit$eph.rate)

## [1] 9.857143

## Percent of brome seedlings becoming established
mean(recruit$brome.prop.begin)

## [1] 51.36429